Problem: Rewrite as a simplified fraction. ${2.\overline{98} = {?}}$
Solution: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}100x &= 298.9898...\\ 1x &= 2.9898...\end{align*}}$ Subtracting the two equations, we have: ${99x = 296}$ ${x = \dfrac{296}{99}} \text{or} {2 \dfrac{98}{99}}$